Transcript for Mysterious Phone Call Gives Hope for Family Lost at Sea

Now, to the american family lost at sea, vanishing with the crew of their boat, while traveling from new zealand to australia. They went missing at the beginning of the month. Now, a mysterious phone call is raising hope they're still alive. Dan harris is back with that story. Such a tough story. The family is holding out hope. Overnight, search officials in new zealand made ominous pronouncements. They now believe the ship did sink. Good morning, america. This is david. Reporter: David dike is an experienced captain. Here he is on his schooner, "the naina," during a crossing in 1990. This morning, he is lost at sea with his wife, his teenage son and a crew of four people. The last time anybody spoke to THEM WAS ON JUNE 3rd, AS THEY Traveled from northern new zealand to australia. A 73-year-old crew member made a satellite phone call to METEOROLOGIST bob McDavitt in new zealand. They were avoiding the incoming storm. They knew they had to brace for it. Reporter: The next day, McDAVITT GOT A TEXT, ANY UPDATE For naina? The conditions were terrible. 68-mile-per-hour winds, 26-foot waves. The family had been on an around-the-world trip for five years. This was to be their final outing. David dike's sister said if anybody can handle rough waters, it's her brother. He's been a ship captain all his life. Reporter: One thing giving the family hope, a mysterious PHONE CALL PLACED ON JUNE 13th. There was a lot of static. She heard her name. And it cut out, died. We think that's it. Reporter: Rescue officials in new zealand say it is possible the boat simply lost communication and drifted offcourse. But they are sounding increasingly certain that "the naina" sank. Probably around about the 4th of june. Reporter: To be clear, the searchers say they have not given up hope of finding survivors. They say it is possible that the crew is on lifeboats or swam to shore. But today, officials mounted their third aerial search and found nothing. They are plotting their next move.

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